Heterogeneous group decision making with thermodynamical parameters

Figures & data

Figure 1. Shapes of $F(\xi )$ with a decision maker’s different sensitive attitudes towards the accuracy of decision values.

Source: Authors.

Table 1. The correlations between the rankings with the original weights and the rectified weights with different sensitive attitudes.

Correlation coefficients	Decision matrices 4*4	Decision matrices 5*5	Decision matrices 6*6	Decision matrices 7*7	Decision matrices 8*8	Decision matrices 9*9	Decision matrices 10*10
Neutrally sensitive (measured by function $F(\xi )=\xi$)	0.950 Sig. 0.000 (2-tailed)	0.995 Sig. 0.000 (2-tailed)	0.997 Sig. 0.000 (2-tailed)	1.000 Sig. 0.000 (2-tailed)	1.000 Sig. 0.000 (2-tailed)	1.000 Sig. 0.000 (2-tailed)	1.000 Sig. 0.000 (2-tailed)
Sensitive (measured by function $F(\xi )=e^{\xi }-1$)	0.895 Sig. 0.000 (2-tailed)	0.916 Sig. 0.000 (2-tailed)	0.915 Sig. 0.000 (2-tailed)	0.914 Sig. 0.000 (2-tailed)	0.894 Sig. 0.000 (2-tailed)	0.906 Sig. 0.000 (2-tailed)	0.921 Sig. 0.000 (2-tailed)
Insensitive (measured by function $F(\xi )=\hspace{0.17em}\text{ln}\hspace{0.17em}(\xi +1)$)	1.000 Sig. 0.000 (2-tailed)	1.000 Sig. 0.000 (2-tailed)	1.000 Sig. 0.000 (2-tailed)	1.000 Sig. 0.000 (2-tailed)	1.000 Sig. 0.000 (2-tailed)	1.000 Sig. 0.000 (2-tailed)	1.000 Sig. 0.000 (2-tailed)

Source: Authors.

Figure 2. Different optimal selections with rectified weights and original weights.

Source: Authors.

Table 2. Decision matrices of the green supplier selection problem.

	$C_1$	$C_2$	$C_3$	$C_4$	$C_5$
Head 1
Supplier 1	$s_6$	0.95	$\left\{s_5,s_6,s_7\right\}$	$s_6$	7
Supplier 2	$s_6$	0.90	$\left\{s_5,s_6\right\}$	$s_7$	9
Supplier 3	$s_4$	0.92	$\left\{s_6,s_7\right\}$	$s_7$	10
Supplier 4	$s_5$	0.88	$\left\{s_5,s_6,s_7\right\}$	$s_5$	10
Head 2
Supplier 1	$s_6$	0.95	$\left\{s_5,s_6\right\}$	$s_5$	9
Supplier 2	$s_7$	0.90	$\left\{s_4,s_5,s_6\right\}$	$s_7$	9
Supplier 3	$s_4$	0.92	$\left\{s_5\right\}$	$s_6$	11
Supplier 4	$s_5$	0.88	$\left\{s_6,s_7\right\}$	$s_6$	10
Head 3
Supplier 1	$s_7$	0.95	$\left\{s_7\right\}$	$s_6$	8
Supplier 2	$s_7$	0.90	$\left\{s_4,s_5\right\}$	$s_6$	9
Supplier 3	$s_4$	0.92	$\left\{s_4,s_5\right\}$	$s_6$	11
Supplier 4	$s_6$	0.88	$\left\{s_6,s_7\right\}$	$s_6$	11

Source: Authors.

Table 3. Thermodynamical feature decision matrix of the green supplier selection problem.

	$C_1$	$C_2$	$C_3$	$C_4$	$C_5$
Supplier 1	$s_{1.25}$	0.23	$\left\{s_{0.76},s_{0.79},s_{0.86}\right\}$	$s_{1.12}$	1.59
Supplier 2	$s_{1.31}$	0.23	$\left\{s_{0.56},s_{0.59},s_{0.73}\right\}$	$s_{1.32}$	1.96
Supplier 3	$s_{0.71}$	0.22	$\left\{s_{0.63},s_{0.72}\right\}$	$s_{1.25}$	2.27
Supplier 4	$s_{1.06}$	0.21	$\left\{s_{0.74},s_{0.78},s_{0.91}\right\}$	$s_{1.12}$	2.25

Note: we normalize the HFLTSs by pessimistic principle, which means $\eta =0.$

Source: Authors.

Table 4. Decision results of the green supplier selection problem.

Dominance degree	Supplier 1	Supplier 2	Supplier 3	Supplier 4	Global value	Ranking
Supplier 1	0	−0.47	−0.31	−0.30	0	4
Supplier 2	0.18	0	−0.21	−0.23	1	1
Supplier 3	−0.11	−0.37	0	−0.12	0.59	2
Supplier 4	−0.09	−0.30	−0.22	0	0.57	3

Source: Authors.